Mika, M.L., Hughes, T.J.R., Schillinger, D., Wriggers, P., & Hiemstra, R.R. (2021). A matrix-free isogeometric Galerkin method for Karhunen-Loève approximation of random fields using tensor product splines, tensor contraction and interpolation based quadrature. Computer Methods in Applied Mechanics and Engineering, 379. June.
Jahanbin, R., & Rahman, S. (2019). An isogeometric collocation method for efficient random field discretization. International Journal for Numerical Methods in Engineering, 117(3), 344–369. January.
Ghanem, R. G., & Spanos, P. D. (1991). Stochastic finite elements: A spectral approach. New York, NY: Springer.
Keese, A. (2003). A review of recent developments in the numerical solution of stochastic partial differential equations (Stochastic Finite Elements). Braunschweig, Institut für Wissenschaftliches Rechnen.
Stefanou, G. (2009). The stochastic finite element method: Past, present and future. Computer Methods in Applied Mechanics and Engineering, 198, 1031–1051.
Sudret, B., & Kuyreghian, A. (2000). Stochastic finite element methods and reliability: A state-of-the-art report. Berkeley: Department of Civil and Environmental Engineering, University of California.
Lu, K., Jin, Y., Chen, Y., Yang, Y., Hou, L., Zhang, Z., Li, Z., & Fu, C. (2019). Review for order reduction based on proper orthogonal decomposition and outlooks of applications in mechanical systems. Mechanical Systems and Signal Processing, 123, 264–297. May.
Rathinam, M., & Petzold, L. R. (2003). A new look at proper orthogonal decomposition. SIAM Journal on Numerical Analysis, 41(5), 1893–1925. January.
Jolliffe, I. T., & Cadima, J. (2016). Principal component analysis: A review and recent developments. Philosophical Transactions of the Royal Society A, 374(2065). April.
Liang, Y. C., Lee, H. P., Lim, S. P., Lin, W. Z., Lee, K. H., & Wu, C. G. (2002). Proper orthogonal decomposition and its applications-Part I: Theory. Journal of Sound and Vibration, 252(3), 527–544. May.
Eiermann, M., Ernst, O. G., & Ullmann, E. (2007). Computational aspects of the stochastic finite element method. Computing and Visualization in Science, 10(1), 3–15. February.
Saad, Y. (2011). Numerical methods for large eigenvalue problems. In Number 66 in Classics in applied mathematics. Society for Industrial and Applied Mathematics, Philadelphia, rev. ed.
Atkinson, K. E. (1997). The numerical solution of integral equations of the second kind 1st ed. Cambridge University Press.
Rahman, S. (2018). A Galerkin isogeometric method for Karhunen-Loève approximation of random fields. Computer Methods in Applied Mechanics and Engineering, 338, 533–561.
Bressan, A., & Takacs, S. (2019). Sum factorization techniques in isogeometric analysis. Computer Methods in Applied Mechanics and Engineering, 352, 437–460. August.
Auricchio, F., Beirão Da Veiga, L., Hughes, T. J. R., Reali, A., Sangalli, G. (2010). Isogeometric collocation methods. Mathematical Models and Methods in Applied Sciences, 20(11), 2075–2107.
Schillinger, D., Evans, J. A., Reali, A., Scott, M. A., & Hughes, T. J. R. (2013). Isogeometric collocation: Cost comparison with Galerkin methods and extension to adaptive hierarchical NURBS discretizations. Computer Methods in Applied Mechanics and Engineering, 267, 170–232.